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Nonsmooth Analysis

2007-05-26 Mathematics
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Release : 2007-05-26
Genre : Mathematics
Kind : eBook
Book Rating : 336/5 ( reviews)

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Book Synopsis Nonsmooth Analysis by : Winfried Schirotzek

Download or read book Nonsmooth Analysis written by Winfried Schirotzek. This book was released on 2007-05-26. Available in PDF, EPUB and Kindle. Book excerpt: This book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and then presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed: this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. Each chapter ends with bibliographic notes and exercises.

Nonsmooth Analysis and Control Theory

2008-01-10 Mathematics
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Release : 2008-01-10
Genre : Mathematics
Kind : eBook
Book Rating : 257/5 ( reviews)

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Book Synopsis Nonsmooth Analysis and Control Theory by : Francis H. Clarke

Download or read book Nonsmooth Analysis and Control Theory written by Francis H. Clarke. This book was released on 2008-01-10. Available in PDF, EPUB and Kindle. Book excerpt: A clear and succinct presentation of the essentials of this subject, together with some of its applications and a generous helping of interesting exercises. Following an introductory chapter with a taste of what is to come, the next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject, leading to an efficient, natural, and powerful body of theory. The whole is rounded off with a self-contained introduction to the theory of control of ordinary differential equations. The authors have incorporated a number of new results which clarify the relationships between the different schools of thought in the subject, with the aim of making nonsmooth analysis accessible to a wider audience. End-of-chapter problems offer scope for deeper understanding.

An Introduction to Nonsmooth Analysis

2013-11-26 Mathematics
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Release : 2013-11-26
Genre : Mathematics
Kind : eBook
Book Rating : 253/5 ( reviews)

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Book Synopsis An Introduction to Nonsmooth Analysis by : Juan Ferrera

Download or read book An Introduction to Nonsmooth Analysis written by Juan Ferrera. This book was released on 2013-11-26. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth Analysis is a relatively recent area of mathematical analysis. The literature about this subject consists mainly in research papers and books. The purpose of this book is to provide a handbook for undergraduate and graduate students of mathematics that introduce this interesting area in detail. - Includes different kinds of sub and super differentials as well as generalized gradients - Includes also the main tools of the theory, as Sum and Chain Rules or Mean Value theorems - Content is introduced in an elementary way, developing many examples, allowing the reader to understand a theory which is scattered in many papers and research books

Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control

1992-05-07 Mathematics
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Release : 1992-05-07
Genre : Mathematics
Kind : eBook
Book Rating : 414/5 ( reviews)

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Book Synopsis Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control by : Marko M Makela

Download or read book Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control written by Marko M Makela. This book was released on 1992-05-07. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.

Introduction to Functional Analysis

2020-11-30 Mathematics
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Release : 2020-11-30
Genre : Mathematics
Kind : eBook
Book Rating : 840/5 ( reviews)

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Book Synopsis Introduction to Functional Analysis by : Christian Clason

Download or read book Introduction to Functional Analysis written by Christian Clason. This book was released on 2020-11-30. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing. This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.

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